Finite Group Databasebeta

← #25022072

Subgroups — #25022072

Order 11008.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic43C211yesmaximal, characteristic
2C2×#14582798C211yesmaximal, characteristic, complemented
3C2×#14582792C211yesmaximal, characteristic, complemented
4C2×#14582774C211yesmaximal, characteristic, complemented
5C2×#14582774C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
7#19132844C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic, complemented
9#19132836C211yesmaximal, characteristic
10#19132832C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132827C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#394C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×D4×Dic43—24no—
19C2×D4×Dic43—24no—
20C2×D4×Dic43—24no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582798—24no—
35#14582792—24no—
36#14582774—24no—
37#14582774—24no—
38C22⋊C4×Dic43—24no—
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C43×#394C418yescomplemented
59C2×#95×C43C2211yescharacteristic
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43—22no—
65C23×Dic43—22no—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—41no—
70C23×Dic43—41no—
71C23×Dic43—41no—
72C23×Dic43—41no—
73C23×Dic43D414yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82D4×Dic43—232no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—22no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43D414yes—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43—41no—
111C2×C22⋊Dic43—41no—
112C2×C22⋊Dic43D414yes—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—41no—
121C2×C4×Dic43—41no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—41no—
134C43⋊#95D414yescomplemented
135C25×C43C2311yescharacteristic
136C25×C43C2311yescharacteristic
137C22×D4×C43—22no—
138C22×D4×C43—22no—
139C22×D4×C43—22no—
140C22×D4×C43—22no—
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43C2×C414yes—
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43C2×C414yescomplemented
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—22no—
160C2×C22⋊C4×C43C2×C414yescomplemented
161C2×C22⋊C4×C43C2×C414yescomplemented
162C2×C22⋊C4×C43C2×C414yescomplemented
163C2×C22⋊C4×C43C2×C414yescomplemented
164#95×C43C2×C414yescomplemented
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43C22×C412yes—
190C24×C43C22×C412yes—
191C24×C43C2×D412yes—
192C24×C43C2×D412yes—
193C24×C43#4112yes—
194C24×C43#4112yes—
195C24×C43C2411yescharacteristic
196C2×D4×C43—28no—
197C2×D4×C43—28no—
198C2×D4×C43—28no—
199C2×D4×C43—28no—
200C2×D4×C43—28no—
201C2×D4×C43—28no—
202C2×D4×C43—28no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C22×C412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×Dic43—28no—
239C22×Dic43—28no—
240C22×Dic43—28no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—44no—
288C22×Dic43—44no—
289C22×Dic43—44no—
290C22×Dic43—44no—
291C22×Dic43—44no—
292C22×Dic43—44no—
293C22×Dic43—44no—
294C22×Dic43—44no—
295C22×Dic43—44no—
296C22×Dic43—44no—
297C22×Dic43—44no—
298C22×Dic43C2×D412yes—
299C22×Dic43C2×D412yes—
300C22×Dic43C2×D412yes—
301C22×Dic43C2×D412yes—
302C22×Dic43C2×D412yes—
303C22×Dic43C2×D412yes—
304C22×Dic43C2×D412yes—
305C22×Dic43C2×D412yes—
306C22×Dic43#4112yes—
307C22×Dic43#4112yes—
308C4⋊C4×C43—28no—
309C22⋊C4×C43—28no—
310C22⋊C4×C43—28no—
311C22⋊C4×C43—28no—
312C22⋊C4×C43—28no—
313C22⋊Dic43—28no—
314C22⋊Dic43—28no—
315C22⋊Dic43—28no—
316C22⋊Dic43—44no—
317C22⋊Dic43—44no—
318C22⋊Dic43—44no—
319C4⋊Dic43—28no—
320C4⋊Dic43—44no—
321C4⋊Dic43—44no—
322C4⋊Dic43—44no—
323C4×Dic43—28no—
324C4×Dic43—44no—
325C4×Dic43—44no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43C4×D414yes—
395C23×C43C4×D414yes—
396C23×C43C23×C411yescharacteristic
397C23×C43C22×D411yescharacteristic
398C23×C43C22×D411yescharacteristic
399C23×C43C22×D411yescharacteristic
400C23×C43C22×D411yescharacteristic
401C23×C43C2×#4111yescharacteristic
402C23×C43C2×#4111yescharacteristic
403C23×C43C2×#4111yescharacteristic
404C23×C43C2×#4111yescharacteristic
405C23×C43C2×#4111yescharacteristic
406C23×C43C2×#4111yescharacteristic
407C23×C43H(5,𝔽2)11yescharacteristic
408C23×C43H(5,𝔽2)11yescharacteristic
409C23×C432−1+411yescharacteristic
410C23×C432−1+411yescharacteristic
411D4×C43—232no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43C4×D414yes—
446C2×C4×C43C4×D414yescomplemented
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—416no—
472C2×Dic43—416no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43#12014yes—
504C2×Dic43#12114yes—
505#14185—431nomaximal, Sylow
506C22×C43—24no—
507C22×C43—24no—
508C22×C43—24no—
509C22×C43—24no—
510C22×C43—24no—
511C22×C43—24no—
512C22×C43—42no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43—42no—
530C22×C43—42no—
531C22×C43—42no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43C2×C4×D411yescharacteristic
537C22×C43C2×C4×D411yescharacteristic
538C22×C43C2×C4×D411yescharacteristic
539C22×C43C2×C4×D411yescharacteristic
540C22×C43C4×#4111yescharacteristic
541C22×C43#52011yescharacteristic
542C22×C43#52011yescharacteristic
543C22×C43C2×#12011yescharacteristic
544C22×C43C2×#12111yescharacteristic
545C22×C43#52511yescharacteristic
546C22×C43#52511yescharacteristic
547C22×C43#52511yescharacteristic
548C22×C43#52511yescharacteristic
549C22×C43#52911yescharacteristic
550C22×C43#53211yescharacteristic
551C22×C43#53411yescharacteristic
552C22×C43#53611yescharacteristic
553C22×C43#53911yescharacteristic
554C22×C43#53911yescharacteristic
555C22×C43D4211yescharacteristic
556C22×C43D4211yescharacteristic
557C22×C43#54611yescharacteristic
558C22×C43#54611yescharacteristic
559C22×C43#54711yescharacteristic
560C22×C43#54711yescharacteristic
561C22×C43#54711yescharacteristic
562C22×C43#54811yescharacteristic
563C22×C43#54811yescharacteristic
564C22×C43#54811yescharacteristic
565C22×C43#55111yescharacteristic
566C22×C43#55211yescharacteristic
567C22×C43#55311yescharacteristic
568C22×C43#55311yescharacteristic
569C22×C43#55611yescharacteristic
570C22×C43#55911yescharacteristic
571C4×C43—24no—
572C4×C43—24no—
573C4×C43—42no—
574C4×C43—42no—
575C4×C43—42no—
576Dic43—24no—
577Dic43—24no—
578Dic43—42no—
579Dic43—42no—
580Dic43—42no—
581Dic43—42no—
582Dic43—81no—
583Dic43—81no—
584C22×C4×D4—431no—
585C2×#394D4311yescharacteristic
586C2×#389—431no—
587C2×#388—431no—
588C2×#385—431no—
589C2×#385—431no—
590C2×C4×C22⋊C4—431no—
591#1440—431no—
592#1439—431no—
593#1438—431no—
594#1437—431no—
595#1436—431no—
596#1436—431no—
597#1436—431no—
598C22⋊#95—431no—
599C2×C43—44no—
600C2×C43—44no—
601C2×C43C4×#12011yescharacteristic
602C2×C43C4×#12111yescharacteristic
603C2×C43#232211yescharacteristic
604C2×C43#235911yescharacteristic
605C2×C43#236111yescharacteristic
606C2×C43#236111yescharacteristic
607C2×C43#236711yescharacteristic
608C2×C43#241011yescharacteristic
609C2×C43#241511yescharacteristic
610C2×C43#243211yescharacteristic
611C2×C43#245511yescharacteristic
612C2×C43#246011yescharacteristic
613C2×C43#246311yescharacteristic
614C2×C43#246611yescharacteristic
615C2×C43#260211yescharacteristic
616C23×D4C2×D4311yescharacteristic
617C24×C4—431no—
618C24×C4—431no—
619C2×C4×D4—864no—
620C2×C4×D4—864no—
621C2×C4×D4—864no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C4⋊C4—431no—
625C22×C4⋊C4—431no—
626C22×C4⋊C4C2×D4311yescharacteristic
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4C2×D4311yescharacteristic
634C22×C22⋊C4C2×D4311yescharacteristic
635C22×C22⋊C4C2×D4311yescharacteristic
636C22×C22⋊C4C2×D4311yescharacteristic
637C22×C42—431no—
638C22×C42—431no—
639C22×C42—431no—
640#394Dic4318yescomplemented
641#389—864no—
642#388—864no—
643#385—864no—
644#385—864no—
645C4×C22⋊C4—864no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—431no—
659C2×#95C2×D4311yescharacteristic
660C43#1418511yescharacteristic, complemented, Sylow
661C25C22×D4311yescharacteristic
662C25C22×D4311yescharacteristic
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4—22no—
668C22×D4—22no—
669C22×D4C2×Dic4314yes—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—431no—
675C23×C4—431no—
676C23×C4—434no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—862no—
680C23×C4—862no—
681C23×C4—862no—
682C23×C4—862no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—862no—
687C23×C4—862no—
688C23×C4—1721no—
689C23×C4—1721no—
690C23×C4—1721no—
691C23×C4—1721no—
692C23×C4C22×D4311yescharacteristic
693C23×C4C22×D4311yescharacteristic
694C23×C4C22×D4311yescharacteristic
695C23×C4C22×D4311yescharacteristic
696C23×C4C22×D4311yescharacteristic
697C4×D4—8632no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—434no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—862no—
703C2×C4⋊C4—862no—
704C2×C4⋊C4—862no—
705C2×C4⋊C4—862no—
706C2×C4⋊C4—862no—
707C2×C4⋊C4—862no—
708C2×C4⋊C4—862no—
709C2×C4⋊C4—862no—
710C2×C4⋊C4—862no—
711C2×C4⋊C4—1721no—
712C2×C4⋊C4C2×Dic4314yescomplemented
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—434no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—1721no—
736C2×C22⋊C4—1721no—
737C2×C22⋊C4—1721no—
738C2×C22⋊C4—1721no—
739C2×C22⋊C4C2×Dic4314yescomplemented
740C2×C22⋊C4C2×Dic4314yescomplemented
741C2×C22⋊C4C2×Dic4314yescomplemented
742C2×C22⋊C4C2×Dic4314yescomplemented
743C2×C42—862no—
744C2×C42—862no—
745C2×C42—862no—
746C2×C42—862no—
747C2×C42—862no—
748C2×C42—862no—
749C2×C42—862no—
750C2×C42—1721no—
751C2×C42—1721no—
752#95—434no—
753#95—862no—
754#95—862no—
755#95—862no—
756#95—862no—
757#95—862no—
758#95—862no—
759#95—862no—
760#95—862no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—1721no—
765#95C2×Dic4314yescomplemented
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24D4×D4312yes—
791C24D4×D4312yes—
792C24#1062190012yes—
793C24#1062190012yes—
794C24C22×Dic4312yes—
795C24C22×Dic4312yes—
796C24C23×D4311yescharacteristic
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—432no—
837C22×C4—432no—
838C22×C4—432no—
839C22×C4—432no—
840C22×C4—868no—
841C22×C4—868no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—868no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—1724no—
890C22×C4—1724no—
891C22×C4—1724no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1724no—
896C22×C4—1724no—
897C22×C4—1724no—
898C22×C4—1724no—
899C22×C4—1724no—
900C22×C4D4×D4312yes—
901C22×C4D4×D4312yes—
902C22×C4#1062190012yes—
903C22×C4#1062190012yes—
904C22×C4C22×Dic4312yes—
905C22×C4C22×Dic4312yes—
906C22×C4C22×Dic4312yes—
907C22×C4C22×Dic4312yes—
908C22×C4C22×Dic4312yes—
909C4⋊C4—28no—
910C4⋊C4—868no—
911C4⋊C4—1724no—
912C4⋊C4—1724no—
913C4⋊C4—1724no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—868no—
919C22⋊C4—868no—
920C22⋊C4—868no—
921C22⋊C4—1724no—
922C22⋊C4—1724no—
923C22⋊C4—1724no—
924C42—868no—
925C42—1724no—
926C42—1724no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23D4×Dic4314yes—
996C23D4×Dic4314yes—
997C23C23×Dic4311yescharacteristic
998C23C2×D4×D4311yescharacteristic
999C23C2×D4×D4311yescharacteristic
1000C23C2×D4×D4311yescharacteristic
1001C23C2×D4×D4311yescharacteristic
1002C23#41×D4311yescharacteristic
1003C23#41×D4311yescharacteristic
1004C23C2×#1062190011yescharacteristic
1005C23C2×#1062190011yescharacteristic
1006C23C2×#1062190011yescharacteristic
1007C23C2×#1062190011yescharacteristic
1008C23#1306337111yescharacteristic
1009C23#1306337111yescharacteristic
1010C23#1306337211yescharacteristic
1011C23#1306337211yescharacteristic
1012D4—232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—434no—
1047C2×C4—434no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—17216no—
1073C2×C4—17216no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4D4×Dic4314yes—
1105C2×C4D4×Dic4314yescomplemented
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22C2×D4×Dic4311yescharacteristic
1137C22C2×D4×Dic4311yescharacteristic
1138C22C2×D4×Dic4311yescharacteristic
1139C22C2×D4×Dic4311yescharacteristic
1140C22#41×Dic4311yescharacteristic
1141C22#1458338211yescharacteristic
1142C22#1458338211yescharacteristic
1143C22#120×D4311yescharacteristic
1144C22#121×D4311yescharacteristic
1145C22#1458340511yescharacteristic
1146C22#1458340511yescharacteristic
1147C22#1458340511yescharacteristic
1148C22#1458340911yescharacteristic
1149C22#1458343011yescharacteristic
1150C22#1458344411yescharacteristic
1151C22#1458346011yescharacteristic
1152C22#1458347111yescharacteristic
1153C22#1458349311yescharacteristic
1154C22#1458349311yescharacteristic
1155C22#1458353311yescharacteristic
1156C22#1458353311yescharacteristic
1157C22#1458354111yescharacteristic
1158C22#1458354211yescharacteristic
1159C22#1458354711yescharacteristic
1160C22#1458354911yescharacteristic
1161C22#1458354911yescharacteristic
1162C22#1458355511yescharacteristic
1163C22#1458355511yescharacteristic
1164C22#1458355711yescharacteristic
1165C22#1458357211yescharacteristic
1166C22#1458358611yescharacteristic
1167C22#1458360111yescharacteristic
1168C22#1458360111yescharacteristic
1169C22#1458361811yescharacteristic
1170C22#1458363111yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—864no—
1177C4—864no—
1178C4—3441no—
1179C4—3441no—
1180C4—1722no—
1181C4—1722no—
1182C4—1722no—
1183C4—1722no—
1184C2—44no—
1185C2—44no—
1186C2#120×Dic4311yescharacteristic
1187C2#121×Dic4311yescharacteristic
1188C2#1913726711yescharacteristic
1189C2#1913759111yescharacteristic
1190C2#1913761511yescharacteristic
1191C2#1913761511yescharacteristic
1192C2#1913767011yescharacteristic
1193C2#1913796411yescharacteristic
1194C2#1913801711yescharacteristic
1195C2#1913821811yescharacteristic
1196C2#1913847311yescharacteristic
1197C2#1913854211yescharacteristic
1198C2#1913858711yescharacteristic
1199C2#1913862611yescharacteristic
1200C2#1914020811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#394C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC2×#394D43
hypocenterC43#14185
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#394

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14582798C2semidirect
3. C2×#14582792C2semidirect
4. C2×#14582774C2semidirect
5. C2×#14582774C2semidirect
6. C2×C22⋊C4×Dic43C2semidirect
7. #19132844C2semidirect
8. #19132840C2semidirect
10. #19132832C2semidirect
11. #19132829C2semidirect
12. #19132829C2semidirect
13. #19132827C2semidirect
14. #19132817C2semidirect
58. C43×#394C4semidirect
134. C43⋊#95D4semidirect
151. C2×C4⋊C4×C43C2×C4semidirect
160. C2×C22⋊C4×C43C2×C4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
162. C2×C22⋊C4×C43C2×C4semidirect
163. C2×C22⋊C4×C43C2×C4semidirect
164. #95×C43C2×C4semidirect
446. C2×C4×C43C4×D4semidirect
640. #394Dic43semidirect
660. C43#14185semidirect
712. C2×C4⋊C4C2×Dic43semidirect
739. C2×C22⋊C4C2×Dic43semidirect
740. C2×C22⋊C4C2×Dic43semidirect
741. C2×C22⋊C4C2×Dic43semidirect
742. C2×C22⋊C4C2×Dic43semidirect
765. #95C2×Dic43semidirect
1105. C2×C4D4×Dic43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D4×Dic432
C2×#145827982
C2×#145827922
C2×#145827742
C2×C22⋊C4×Dic432
#191328442
#191328402
#191328362
#191328322
#191328292
#191328272
#191328172
C2×C43×#3942
#1418543